This is an interesting one. I'm not sure he'd have gone to United. Not because Liverpool is a better job or anything like that; it's the fact that he's gone to a club who aren't currently at an elite level - a real project is required. There's money but not compared to the very richest clubs. This seems to attract Klopp.
Winning the league with Liverpool would be a greater feat than doing it at United. Klopp wants to do it the hard way.
I know Liverpool fans like to romanticise pretty much everything, but I think it was far more of a right place at the right time thing. If the United job had been vacant last October, with Liverpool pressing on with Rodgers, and assuming Mourinho hadn't yet become available, then it's likely Klopp would've got a shot at the job here.
The project to get United back to title winners is almost as big as Liverpool's, and whilst it wouldn't be as big a title win as for Liverpool (due to the timescales since last win), the next manager to get United to win a title will be part of club legend.
Anyway, it won't be Klopp. Hopefully he never wins another league title again (in this country anyway). I think we've a better shot at league success with the other obvious candidate anyway.